Master Degree / Yüksek Lisans Tezleri
Permanent URI for this collectionhttps://hdl.handle.net/11147/3008
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Master Thesis Almost Local-Global Rings(Izmir Institute of Technology, 2017) Susuzlu, İdem; Ay Saylam, BaşakThe main purpose of this thesis is to investigate the Invariant Factor Theorem for Prüfer domains. In accordance with this aim, we give a survey of necessary and su cient conditions on a Prüfer domain to satisfy the Invariant Factor Theorem. In this process, almost local-global rings have important role since they satisfy the USC-property. Regarding to the UCS-property, BCS-rings together with their properties are also investigeted.Master Thesis Krull-Schmidt Properties Over Rings of Finite Character(Izmir Institute of Technology, 2016) Gürbüz, Ezgi; Ay Saylam, BaşakThe main purpose of this thesis is to investigate the notion of Krull-Schmidt properties over rings of finite character. In accordance with this aim, we give a survey of necessary and sufficient conditions on an h-local domain for certain Krull-Schmidt properties hold for direct sums of ideals, direct sums of indecomposable submodules of finitely generated free modules and direct sums of rank one torsion-free modules. By using obtained characterizations, some useful results for Krull-Schmidt properties of modules over Noetherian and Prüfer domains are proven. Besides, the characterizations of Noetherian UDI domains are given.